[ElaineM]

If you are not into alternative therapies would you be able to include various kinds of mushrooms in your diet? They improve the immune system which is a large part part of the white blood count. Would you be willing to eat berries and more veggies to increase your white blood count and improve your immune system?
It would be very easy to make a smoothy with some fresh or frozen berries, other fresh or frozen fruits, yoghurt or almond milk and protein powder. You could even add a little flax meal or a small amount of kale to the smoothy for extra nutrition.
It is too bad you are not willing to consider alternative therapies, because even echinecea and vitamin c can increase the white blood count. Liquid iron with a little orange juice with vitamin c might even do the trick. Vitamin C increases iron absorption and the liquid iron might raise the hemoglobin. Iron pills can cause constipation. Supplements containing mushrooms and astragalus can help increase the white blood count.
Take care. All the best to you.